一维无序系统中特征态的局部化

Progress of Theoretical Physics Supplement Pub Date : 2013-05-16 DOI:10.1143/PTPS.72.232

M. Goda

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摘要

对具有对角和非对角随机的一维无限无序系统的本征态的局部化得到了精确的结果。建立了与多马尔可夫链相关的矩阵乘积的一个furstenberg型定理。因此，Matsuda和Ishii的理论被推广到具有两种随机性的系统。谐波链、紧密结合电子系统和海森堡-马蒂斯模型是典型的例子。

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Localization of Eigenstates in One-Dimensional Disordered Systems

Exact results are obtained on the localization of eigenstates in one dimensional infinite disordered systems with diagonal and off-diagonal random nesses. A Furstenberg-type theorem is established for the product of matrices associated with a multi-Markov-chain. As a result, Matsuda and Ishii's theory is generalized to examine the systems with both randomnesses. Harmonic chains, tightly binding electronic systems and Heisenberg-Mattis model are considered as typical examples.

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